2023/12/29 by Monika E. Pietrzyk, Pietrzyk, Monika E., Cécile Barbachoux +3
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.2312.17474
openalex publication_date 2023/12/29 · openalex created_date 2024/01/02 · openalex updated_date 2026/07/28
The aim of this paper is to understand the relation between the canonical Hamilton-Jacobi equation for Maxwell's electrodynamics, which is an equation with variational derivatives for a functional of field configurations, and the covariant (De Donder-Weyl) Hamilton-Jacobi equation, which is a partial derivative equation on a finite dimensional space of vector potentials and spacetime coordinates. We show that the procedure of spacetime splitting applied to the latter allows us to reproduce both the canonical Hamilton-Jacobi equation and the Gauss law constraint in the Hamilton-Jacobi form without a recourse to the canonical Hamiltonian analysis. Our consideration may help to analyze the quasi-classical limit of the connection between the standard quantization in field theory based on the canonical Hamiltonian formalism with a preferred time dimension and the precanonical quantization that uses the De Donder-Weyl Hamiltonian formulation where space and time dimensions treated equally.